Let `f : R to R : f (x) =|x|` prove that f o f =f

Let R be the set of all real numbers let f: R to R : f(x) = sin x and g : R to R : g (x) =x^(2) . Prove that g o f ne f o g

Let f : R to R ,f (a) =1, f '(a) = 2 then prove that Lt _(x to 0) ((f ^(2) (a + x ) )/( f (a)))^(1/x) = e ^(4)

Let f : R to R : f (x) = (2x -3) " and " g : R to R : g (x) =(1)/(2) (x+3) show that (f o g) = I_(R) = (g o f)

Let f : R to R : f (x) =(2x +1) " and " g : R to R : g (x) =(x^(2) -2) Write down the formulae for (i) ( g o f) (ii) ( f o g) (iii) ( f o f) (iv) ( g o f)

Let f : R to R : f (x) =x^(2) " and " g: R to R : g (x) = (x+1) Show that (g o f) ne (f o g)

Let f : R to R : f (x) =10x +7. Find the function g : R to R : g o f = f o g =I_(g)

Let f : R to R : f (x) = x^(2) + 2 "and " g : R to R : g (x) = (x)/(x-1) , x ne 1 . Find f o g and g o f and hence find (f o g) (2) and ( g o f) (-3)

Let f : R to R : f (x) =(3-x^(3))^(1//3). Find f o f

Let f:R to R where f(x) =sin x. Show that f is into. Also find the codomain if f is onto.

Let f:R to R where f(x) =sin x. Show that f is into. Also find the codomain if f is onto.